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Worksheet 358

A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may ... more

In algebra, the discriminant of a polynomial is a function of its coefficients, typically denoted by a capital 'D’ or the capital Greek letter Delta ... more

Vieta's formulas ( sum of quadratic polynomial roots)

In mathematics, Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.
P(x)=ax^2 + bx + c,

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Solves a univariate polynomial equation of the second degree. This formula will calculate both roots and both real and complex roots.

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Vieta's formulas ( product of quadratic polynomial roots)

In mathematics, Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.
P(x)=ax^2 + bx + c,

... more

Bivariate (two variable) quadratic function(y minimum/maximum)

A bivariate (two variable) quadratic function is a second-degree polynomial which describes a quadratic surface and has the form: f(x,y)=Ax^2 + By^2 + Cx + ... more

Bivariate (two variable) quadratic function(x minimum/maximum)

A bivariate (two variable) quadratic function is a second-degree polynomial which describes a quadratic surface and has the form: f(x,y)=Ax^2 + By^2 + ... more

Minimum or maximum value of the quadratic function

A quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which ... more

Quartic equation

Solves a univariate polynomial equation of the fourth degree. (For possitive values of x)

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Cubic equation

Solves a univariate polynomial equation of the third degree.

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Y-Coordinate of the focus of the parabola of a Quadratic Function

A parabola is a graph of a quadratic function, such as y=ax^2+bx+c. A parabola is the set of all points equidistant from a point that is called the focus ... more

Y-Coordinate of the vertex, of the parabola of a Quadratic Function

Parabolas with axes of symmetry parallel to the y-axis have equations of the form y=ax^2+bx+c.
The x-coordinate and y-coordinate at the vertex can be ... more

Critical point of a cubic function ( local maximum )

A cubic function is a function of the form f(x): ax3 + bx2 + cx + d.
The critical points of a cubic equation are those values of x where the slope of ... more

Critical point of a cubic function ( local minimum )

A cubic function is a function of the form f(x): ax3 + bx2 + cx + d.
The critical points of a cubic equation are those values of x where the slope of ... more

X-Coordinate of the vertex, of the parabola of a Quadratic Function

Parabolas with axes of symmetry parallel to the y-axis have equations of the form y=ax^2+bx+c.
The x-coordinate and y-coordinate at the vertex can be ... more

Root mean square of phase-to-phase voltage

In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. In a balanced ... more

Perfectly inelastic collision

A collision is an isolated event in which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time. Collision is ... more

Synodic Period

The orbital period is the time taken for a given object to make one complete orbit around another object.When mentioned without further qualification in ... more

Drag equation ( for fluids)

Drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) refers to forces acting ... more

Logarithmic Standard Deviation - 2nd moment

Shows how much variation or dispersion from the average exists. Logarithmic mean size (1st moment) needs to be precalculated.

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Geometric Kurtosis - 4th moment

Is a measure that describes the “tailedness” of the probability distribution of a real-valued random variable. Geometric mean size (1st moment) ... more

Arithmetic Standard Deviation - 2nd moment

Shows how much variation or dispersion from the average exists, on the particles’ size distribution of a soil, in metric scale. Arithmetic mean size (1st ... more

Logarithmic Kurtosis - 4th moment

Is a measure that describes tthe “tailedness” of the probability distribution of a real-valued random variable. Particles logarithmic mean size ... more

Colpitts oscillator (frequency)

Colpitts oscillator is an oscillator that uses an LC circuit (also called a resonant circuit, tank circuit, or tuned circuit) combined with a transistor ... more

Kepler's Third Law

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1.The orbit of a ... more

Logarithmic Mean Size - 1st moment

Calculates the logarithmic mean size (moments method) of the particles’ size distribution of a soil, in phi scale

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Richardson Number - thermal convection

The Richardson number (Ri) is named after Lewis Fry Richardson (1881 – 1953). It is the dimensionless number that expresses the ratio of potential to ... more

Standard Gravitational Parameter - Two bodies orbiting each other

In celestial mechanics, the standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of the ... more

Arithmetic mean size - 1st moment

Calculates the arithmetic mean size (arithmetic method of moments) of the particles’ size distribution of a soil, in metric scale. In statistics, the ... more

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